A Hybrid Approximation Method for Integer-Order Approximate Realization of Fractional-Order Derivative Operators

Abstract

The use of fractional-order (FO) calculus for the solution of different problems in many fields has increased recently. However, the usage of FO system models in practice brings some difficulties. The FO operator, fractance device, is usually realized via several integer-order approximation methods, which have pros and cons in the aspect of operation frequency, time response and stability region. These methods may not meet all performance expectations. In this regard, author proposes an efficient hybrid integer-order approximation method for FO derivative operator without causing any additional difficulty in realization. The proposed method combines Matsuda and modified stability boundary locus (M-SBL) approximation methods. The advantage of each method is combined in a single hybrid function by considering root mean square error (RMSE) rates for step response. The performance of hybrid transfer function is analyzed in comparison with Matsuda, Oustaloup, continued fraction expansion (CFE) and M-SBL transfer functions for both frequency and time response. Analog realization of the proposed model is performed experimentally via partial fraction expansion method. Analog design is verified via both Multisim simulations and experimental results. The improvements due to the hybrid behavior and the consistency of experimental results with theoretical and simulation results demonstrate the practicality and usefulness of the hybrid model.